I understand you would need to register the pistol in conjunction with the conversion as an SBR, but would that in turn restrict you from carrying the pistol alone as a concealed weapon? I don't think it would if you didn't have the conversion in your immediate possession, but I'd really like a citing of a definite answer if anyone knows.

Depnds, as this is one of those ATF gray areas.

I've seen a letter from ATF saying that the gun had to be transported and stored in SBR configuration and could only be put back into pistol configuration for a short time at the range. Since the gun is now registered as an SBR (not a 'pistol' anymore) this makes sense.

Others say they have a letter saying it is OK to carry it as a handgun without the stock.

Personally, I'd like to carry the gun as a pistol and one of the snap on stocks in my EDC bag to put on if needed.